Oscillator circuits are commonly used in many electrical systems to generate a repeating waveform at or around an oscillating frequency or fundamental frequency. Oscillator circuits are often used to generate clock signals in digital integrated circuits as a basis to control the timing behavior of other signals.
In oscillator based systems, the oscillator phase uncertainty may severely affect the overall system performance. Phase noise in the oscillator circuit may result in reducing the timing margins in digital systems, and compromising channel separations in communications. Hence, phase noise is a major concern during the oscillator circuit design. Efficient and accurate prediction of oscillator noise is one of the most important functionalities for present simulation and verification tools.
Several phase noise prediction techniques have been suggested for oscillator circuits. Most of these techniques are based on solving for a Perturbation Projection Vector (PPV). The PPV techniques characterize the oscillators' phase response to perturbations.
The PPV-based phase noise prediction techniques predict the oscillator noise correctly for small oscillator circuits. However, as the technology advances, oscillators have become more complex with more devices. These extra devices have made oscillator circuits larger and thus have added time constant (RC delays). The larger oscillator circuits challenge previous noise prediction methods. Large time constants significantly compromise the matrix conditioning of oscillators' linear periodic time-varying (LPTV) systems, making standard PPV noise analysis techniques fail or less accurate.